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Algebraic Attacks on Summation Generators [chapter]

Dong Hoon Lee, Jaeheon Kim, Jin Hong, Jae Woo Han, Dukjae Moon
2004 Lecture Notes in Computer Science  
We apply the algebraic attacks on stream ciphers with memories to the summation generator.  ...  We also show that the techniques of [6, 2] can be applied to summation generators using 2 k LFSRs to reduce the effective degree of the algebraic equation.  ...  Structure of summation generators In this work, we study the summation generator with the algebraic attack in mind.  ... 
doi:10.1007/978-3-540-25937-4_3 fatcat:fgviepljfbd4hbzpxxnpwu5raq

Algebraic Countermeasure to Enhance the Improved Summation Generator with 2-Bit Memory

Md. Iftekhar Salam, Hoon-Jae Lee
2013 Journal of Networks  
This stream cipher was proposed in 2008 to enhance the security of the improved summation generator against the algebraic attack.  ...  Recently proposed algebraic attack has been shown to be very effective on several stream ciphers.  ...  Algebraic attack on stream cipher includes attacks on nonlinear filter generator [2] , attacks on summation generator [4] , attacks on combiners with memory [2] , attacks on mutually clocked shift register  ... 
doi:10.4304/jnw.8.5.977-984 fatcat:kacqzlbwbrds5crrvjr5kemkuu

Methodes de Resolution et de Discussion des Problemes de Geometrie

G. Lemaire
1904 Mathematical Gazette  
This is the German edition of a useful introduction to methods of attacking the solution of geometrical riders.  ...  The second treats of summation, the J. Bernouilli Function, and Euler's summation formula with its applications.  ...  The second treats of summation, the J. Bernouilli Function, and Euler's summation formula with its applications.  ... 
doi:10.2307/3605178 fatcat:xmfgncy5rfhivbktzmontovr4u

The ANF of the Composition of Addition and Multiplication mod 2 n with a Boolean Function [chapter]

An Braeken, Igor Semaev
2005 Lecture Notes in Computer Science  
As an application, the formula for addition modulo 2 n is applied in an algebraic attack on the summation generator and the E0 encryption scheme in the Bluetooth keystream generator.  ...  Compact formulas are derived to represent the Algebraic Normal Form (ANF) of f (x + a mod 2 n ) and f (x × a mod 2 n ) from the ANF of f , where f is a Boolean function on F n 2 and a is a constant of  ...  Algebraic Attack on the Summation Generator Consider a summation generator, proposed by Rueppel [25] , that consists of n binary Linear Feedback Shift Registers (LFSR).  ... 
doi:10.1007/11502760_8 fatcat:5ztssiiyerfa7csxa2ddvt47m4

Generic Analysis of Small Cryptographic Leaks

Itai Dinur, Adi Shamir
2010 2010 Workshop on Fault Diagnosis and Tolerance in Cryptography  
(Dinur&Shamir): Is a very general key derivation algebraic attack Generalizes and improves some previous summation-based attacks such as Integral Attacks and Vielhaber's AIDA Was recently used to break  ...  The attacker can obtain one bit of output for any chosen plaintext.  ...  18 Maxterms for 3-round Serpent: Conclusions: Cube attacks seem to be ideal generic tools in leakage attacks They have the unique property that they can be applied even to poorly understood types of  ... 
doi:10.1109/fdtc.2010.11 dblp:conf/fdtc/DinurS10 fatcat:nnu4sggluzbobgjh4oz623pxe4

Practical attack on NLM-MAC scheme

Mohammad Ali Orumiehchiha, Josef Pieprzyk, Ron Steinfeld
2014 Information Processing Letters  
The NLM stream cipher designed by HoonJae Lee, SangMin Sung, HyeongRag Kim is a strengthened version of the LM summation generator that combines linear and non-linear feedback shift registers.  ...  The attack needs about n 2 key-stream bits. We also show adversary is able forge any MAC tag very efficiently by having only one pair (MAC tag, cipher-text).  ...  Unfortunately, it is insecure against the correlation and algebraic attacks. In 2000, Hoon Jae Leea and Sang Jae Moon proposed an improved summation generator with 2-bit memory (5) .  ... 
doi:10.1016/j.ipl.2014.04.010 fatcat:xz7s4baptjef3fbehjpsranvuq

A novel architecture with scalable security having expandable computational complexity for stream ciphers

Prathap Siddavaatam, Reza Sedaghat
2017 Facta universitatis - series Electronics and Energetics  
Contemporary stream cipher designs are highly vulnerable to algebraic cryptanalysis based on linear algebra, in which the inputs and outputs are formulated as multivariate polynomial equations.  ...  Recently, Addition Modulo has been suggested over logic XOR as a mixing operator to guard against such attacks.  ...  Later, the attack was generalized and applied on stream ciphers and block ciphers [5] [6] [7] .  ... 
doi:10.2298/fuee1704459s fatcat:okt27kydlrcspf6iqawusiy2z4

Page 69 of Mathematical Gazette Vol. 3, Issue 46 [page]

1904 Mathematical Gazette  
The second treats of summation, the J. Bernouilli Function, and Euler’s summation formula with its applications.  ...  Graphs are well to the fore in dealing with equations generally, the theory of the irrational number, derivatives, multiple roots, Sturm’s theorem, and discontinuous functions, The chapter on involution  ... 

Association of Teachers of Mathematics in the Middle States and Maryland. Bulletin No. I

1904 Mathematical Gazette  
The second treats of summation, the J. Bernouilli Function, and Euler's summation formula with its applications.  ...  The second treats of summation, the J. Bernouilli Function, and Euler's summation formula with its applications.  ...  , continued fractions, summation of series, theory of numbers, determinants, and theory of equations.  ... 
doi:10.2307/3605177 fatcat:rkechftcd5bn7fuodu72rl6pba

Aufgaben aus der Niederen Geometrie. By I. Alexandroff. Pp. v, 123. 1904. (Teubner.)

1904 Mathematical Gazette  
The second treats of summation, the J. Bernouilli Function, and Euler’s summation formula with its applications.  ...  Graphs are well to the fore in dealing with equations generally, the theory of the irrational number, derivatives, multiple roots, Sturm’s theorem, and discontinuous functions, The chapter on involution  ... 
doi:10.1017/s0025557200114755 fatcat:xe2pjhdhsjfczaeity5fcj7owu

Lehrbuch der Differenzenrechnung. By D. Seliwanoff. Pp. vi, 92. 1904. (Teubner.)

1904 Mathematical Gazette  
The second treats of summation, the J. Bernouilli Function, and Euler’s summation formula with its applications.  ...  Graphs are well to the fore in dealing with equations generally, the theory of the irrational number, derivatives, multiple roots, Sturm’s theorem, and discontinuous functions, The chapter on involution  ... 
doi:10.1017/s0025557200114767 fatcat:ngt2usneqndxvhbtxiurixlio4

Lehrbuch der Analytischen Geometrie. By O. Fort and O. Schlomilch. Vol. I. Analytische Geometrie der Ebene. 7th edition. Revised by R. Heger. 1904. (Teubner.)

1904 Mathematical Gazette  
The second treats of summation, the J. Bernouilli Function, and Euler’s summation formula with its applications.  ...  Graphs are well to the fore in dealing with equations generally, the theory of the irrational number, derivatives, multiple roots, Sturm’s theorem, and discontinuous functions, The chapter on involution  ... 
doi:10.1017/s0025557200114779 fatcat:iheeet2gpbftnnaamqwwyawrpe

A New Method for Geometric Interpretation of Elliptic Curve Discrete Logarithm Problem [article]

Daniele Di Tullio, Ankan Pal
2019 arXiv   pre-print
In cryptography, this interpretation can be used to design attacks on EC-DLP.  ...  Presently, the best known attack algorithm having a sub-exponential time complexity is through the implementation of Summation Polynomials and Weil Descent.  ...  We would like to thank the High Performance Computing (HPC) facility of University of L'Aquila, which enabled us to implement our algorithm on MAGMA and run the experiments to validate our results.  ... 
arXiv:1909.08901v1 fatcat:j3u4gljhxjehhikcmvflwq3yqu

A Simple Algebraic Representation of Rijndael [chapter]

Niels Ferguson, Richard Schroeppel, Doug Whiting
2001 Lecture Notes in Computer Science  
We show that there is a very straightforward closed algebraic formula for the Rijndael block cipher.  ...  This formula is highly structured and far simpler then algebraic formulations of any other block cipher we know.  ...  There are some general techniques that work for any block cipher, but these do not lead to practical attacks.  ... 
doi:10.1007/3-540-45537-x_8 fatcat:6moz65bmozgmxhj7b2wo7pkfi4

Advanced Course in Algebra

W. Wells
1904 Mathematical Gazette  
The second treats of summation, the J. Bernouilli Function, and Euler's summation formula with its applications.  ...  This is the German edition of a useful introduction to methods of attacking the solution of geometrical riders.  ...  The second treats of summation, the J. Bernouilli Function, and Euler's summation formula with its applications.  ... 
doi:10.2307/3605179 fatcat:lk2htzc4mjhf7hzpvjrcmrsf7a
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